No longer represents its drawing the way of action (as the switch symbol still did similar to an Egyptian hieroglyph). It is an empty sleeve getting its contents and meaning only by definition, similar to the fact that our Latin letters give no hint how to spell them. Five important types are presented here, a speciality is the inverter, always giving as result the opposite of its (single) input.
The gate symbol gives us only evidence of what it does, nothing about how it is done.
But we have seen how it could be done.
And we have seen (by the adder) how important a sight from several sides on the same object can be!
By the way, we can see the (half)-adder (not necessarily!) as a combination of AND and XOR. By this way it is easier to understand. A full adder with additional input and output to manage the "carry" is so complicated that gate symbols are nearly indispensable to understand it.

But we should never forget: The gate symbols are nothing but symbols for the working of a (mostly transistor) layout. Though you may buy them as discrete chips - in a modern computer you will scarcely find them!


move on